\contentsline {chapter}{\numberline {1}重力波の基礎理論}{1}
\contentsline {section}{\numberline {1.1}はじめに}{1}
\contentsline {section}{\numberline {1.2}表面重力波}{1}
\contentsline {subsection}{\numberline {1.2.1}表面重力波の定式化}{1}
\contentsline {subsubsection}{● 速度ポテンシャルの導入}{2}
\contentsline {subsubsection}{● 連続の式}{2}
\contentsline {subsubsection}{● 境界条件}{2}
\contentsline {subsubsection}{● 表面重力波の解の導出}{3}
\contentsline {subsection}{\numberline {1.2.2}表面重力波の分散関係式}{5}
\contentsline {subsection}{\numberline {1.2.3}表面重力波の圧力成分}{5}
\contentsline {subsection}{\numberline {1.2.4}浅水波・深水波近似}{6}
\contentsline {subsubsection}{● 深水波近似}{6}
\contentsline {subsubsection}{● 浅水波近似}{7}
\contentsline {subsection}{\numberline {1.2.5}表面重力波の波のエネルギーとフラックス}{8}
\contentsline {subsubsection}{● 表面重力波の波のエネルギー}{8}
\contentsline {subsubsection}{● 表面重力波の波のエネルギーフラックス}{10}
\contentsline {section}{\numberline {1.3}群速度とエネルギーフラックス}{11}
\contentsline {subsection}{\numberline {1.3.1}群速度}{11}
\contentsline {subsubsection}{● $c_{g}< c$ の場合}{12}
\contentsline {subsubsection}{● $c_{g}> c$ の場合}{12}
\contentsline {subsection}{\numberline {1.3.2}波束と群速度}{12}
\contentsline {subsection}{\numberline {1.3.3}群速度とエネルギーフラックス}{14}
\contentsline {section}{\numberline {1.4}波線理論}{14}
\contentsline {subsection}{\numberline {1.4.1}深さ $H$ が一定の場合}{14}
\contentsline {subsection}{\numberline {1.4.2}深さ $H$ が変化する場合}{15}
\contentsline {chapter}{\numberline {2}非回転系重力波 1 − 浅水重力波}{17}
\contentsline {section}{\numberline {2.1}浅水重力波(Shallow-Water Gravity Waves)}{17}
\contentsline {subsection}{\numberline {2.1.1}浅水重力波の定性的な特徴}{17}
\contentsline {subsection}{\numberline {2.1.2}浅水重力波の定性的な伝播メカニズム}{17}
\contentsline {subsection}{\numberline {2.1.3}浅水重力波の定式化}{18}
\contentsline {chapter}{\numberline {3}非回転系重力波 2 − 内部重力波}{21}
\contentsline {section}{\numberline {3.1}内部重力波(Internal Gravity (Buoyancy) Waves)}{21}
\contentsline {subsection}{\numberline {3.1.1}大気重力波の定性的な特徴}{21}
\contentsline {subsection}{\numberline {3.1.2}純粋な内部重力波(パーセル法による解釈)}{21}
\contentsline {subsection}{\numberline {3.1.3}純粋な内部重力波の定式化}{22}
\contentsline {subsection}{\numberline {3.1.4}内部重力波の分散関係}{24}
\contentsline {subsection}{\numberline {3.1.5}内部重力波の構造と伝搬メカニズム}{25}
\contentsline {subsection}{\numberline {3.1.6}地形性の内部重力波}{26}
\contentsline {subsection}{\numberline {3.1.7}地形性内部重力波の定式化}{26}
\contentsline {subsection}{\numberline {3.1.8}地形性内部重力波の分散関係式}{26}
\contentsline {subsection}{\numberline {3.1.9}地形性内部重力波の鉛直構造と鉛直伝播可能性}{27}
\contentsline {chapter}{\numberline {4}重力波(回転系)}{29}
\contentsline {section}{\numberline {4.1}はじめに}{29}
\contentsline {section}{\numberline {4.2}基礎方程式の定式化(浅水方程式)}{29}
\contentsline {subsection}{\numberline {4.2.1}圧力傾度力}{29}
\contentsline {subsection}{\numberline {4.2.2}連続の式}{30}
\contentsline {subsection}{\numberline {4.2.3}基礎方程式}{30}
\contentsline {section}{\numberline {4.3}浅水方程式における高周波・低周波レジーム}{31}
\contentsline {subsection}{\numberline {4.3.1}$\omega \gg f$ (高周波)の場合}{32}
\contentsline {subsection}{\numberline {4.3.2}$\omega > f$ (ただし $\omega \sim f$)の場合}{32}
\contentsline {subsection}{\numberline {4.3.3}$\omega \ll f$ (低周波)の場合}{32}
\contentsline {section}{\numberline {4.4}回転系の重力波}{33}
\contentsline {chapter}{\numberline {5}慣性重力波}{34}
\contentsline {section}{\numberline {5.1}慣性重力波(Inertio-Gravity Waves)}{34}
\contentsline {subsection}{\numberline {5.1.1}慣性重力波の定性的な特徴}{34}
\contentsline {subsection}{\numberline {5.1.2}パーセル法による慣性重力波の解釈}{34}
\contentsline {subsection}{\numberline {5.1.3}慣性重力波の定式化}{36}
\contentsline {subsection}{\numberline {5.1.4}慣性重力波の分散関係}{37}
\contentsline {subsection}{\numberline {5.1.5}慣性重力波の構造と伝搬メカニズム}{37}
\contentsline {chapter}{\numberline {6}ケルビン波}{39}
\contentsline {section}{\numberline {6.1}ケルビン波}{39}
\contentsline {subsection}{\numberline {6.1.1}ケルビン波の定式化}{39}
\contentsline {subsection}{\numberline {6.1.2}ケルビン波の分散関係}{40}
\contentsline {subsection}{\numberline {6.1.3}ケルビン波の構造}{41}
\contentsline {chapter}{\numberline {7}ロスビー波}{42}
\contentsline {section}{\numberline {7.1}ロスビー波}{42}
\contentsline {subsection}{\numberline {7.1.1}準地衝流渦度方程式}{42}
\contentsline {subsection}{\numberline {7.1.2}ロスビー波の分散関係式}{43}
\contentsline {chapter}{\numberline {8}浅水系の赤道波の定式化と無次元化}{46}
\contentsline {section}{\numberline {8.1}定式化}{46}
\contentsline {section}{\numberline {8.2}無次元化}{46}
\contentsline {section}{\numberline {8.3}$ v$ の式の導出}{48}
\contentsline {section}{\numberline {8.4}境界条件}{48}
\contentsline {chapter}{\numberline {9}赤道波の固有値問題とその解}{50}
\contentsline {section}{\numberline {9.1}固有値問題の定式化}{50}
\contentsline {section}{\numberline {9.2}$\mathaccent "705E {v}\not =0$ の場合}{51}
\contentsline {subsection}{\numberline {9.2.1}$n=0$ の場合}{52}
\contentsline {subsection}{\numberline {9.2.2}$n\ge 1$ の場合}{54}
\contentsline {section}{\numberline {9.3}$\mathaccent "705E {v}=0$ の場合}{56}
\contentsline {subsection}{\numberline {9.3.1}$\omega = -k (\not =0)$ の場合}{57}
\contentsline {subsection}{\numberline {9.3.2}$\omega = k$ の場合}{57}
\contentsline {section}{\numberline {9.4}固有値, 固有関数のまとめ}{58}
\contentsline {subsection}{\numberline {9.4.1}$ \mathaccent "705E {v}\not =0$ の解}{58}
\contentsline {subsection}{\numberline {9.4.2}$ \mathaccent "705E {v}=0$ の解}{59}
\contentsline {section}{\numberline {9.5}位相速度のまとめ}{59}
\contentsline {subsection}{\numberline {9.5.1}$ \mathaccent "705E {v}\not =0$ の解}{59}
\contentsline {subsection}{\numberline {9.5.2}$ \mathaccent "705E {v}=0$ の解}{60}
\contentsline {chapter}{\numberline {10}赤道波の分散関係式と水平構造}{61}
\contentsline {section}{\numberline {10.1}赤道波の分散曲線}{61}
\contentsline {section}{\numberline {10.2}$n=-1$ の場合の水平構造}{62}
\contentsline {section}{\numberline {10.3}$n=0$ の場合の水平構造}{63}
\contentsline {section}{\numberline {10.4}$n\ge 1$ の場合の水平構造}{64}
\contentsline {section}{\numberline {10.5}$k=0$ のモードの水平構造に関する注釈}{66}
\contentsline {chapter}{\numberline {11}慣性重力波の水平伝播のメカニズム}{69}
\contentsline {section}{\numberline {11.1}$ n=1, k=0$ の慣性重力波}{69}
\contentsline {subsection}{\numberline {11.1.1}$n=1, k=0$ の慣性重力波の特徴}{70}
\contentsline {subsection}{\numberline {11.1.2}$n=1, k=0$ の慣性重力波の構造を決める物理量}{71}
\contentsline {subsection}{\numberline {11.1.3}$n=1, k=0$ の慣性重力波の構造}{72}
\contentsline {section}{\numberline {11.2}$ n=1, k\not =0$ の東進慣性重力波}{79}
\contentsline {subsection}{\numberline {11.2.1}$ 0 < k \le 1.2$ (低波数)の東進慣性重力波の特徴}{79}
\contentsline {subsection}{\numberline {11.2.2}$ k > 1.2$ (高波数)の東進慣性重力波の特徴}{88}
\contentsline {section}{\numberline {11.3}$ n=1, k\not =0$ の西進慣性重力波}{91}
\contentsline {subsection}{\numberline {11.3.1}$ 0 < k \le 1.1$ (低波数)の西進慣性重力波の特徴}{91}
\contentsline {subsection}{\numberline {11.3.2}$ k > 1.1$ (高波数)の西進慣性重力波の特徴}{95}
\contentsline {section}{\numberline {11.4}$ n=2, k=0$ の慣性重力波}{97}
\contentsline {subsection}{\numberline {11.4.1}$n=2, k=0$ の慣性重力波の特徴}{97}
\contentsline {subsection}{\numberline {11.4.2}$n=2, k=0$ の慣性重力波の構造}{98}
\contentsline {section}{\numberline {11.5}$ n=2, k\not =0$ の東進慣性重力波}{104}
\contentsline {section}{\numberline {11.6}$ n=2, k\not =0$ の西進慣性重力波}{108}
\contentsline {chapter}{\numberline {12}赤道ロスビー波の水平伝播のメカニズム}{112}
\contentsline {section}{\numberline {12.1}$ n=1, k=0$ の赤道ロスビー波}{113}
\contentsline {section}{\numberline {12.2}$ n=1, k\not =0$ の赤道ロスビー波}{113}
\contentsline {subsection}{\numberline {12.2.1}$ 0 < k \le 2.0$ (低波数)の場合}{113}
\contentsline {subsection}{\numberline {12.2.2}$ k > 2.0$ (高波数)の場合}{118}
\contentsline {chapter}{\numberline {13}混合ロスビー重力波の水平伝播のメカニズム}{125}
\contentsline {section}{\numberline {13.1}$n=0, k=0$ の混合ロスビー重力波}{125}
\contentsline {subsection}{\numberline {13.1.1}$n=0, k=0$ の混合ロスビー重力波の特徴}{126}
\contentsline {subsection}{\numberline {13.1.2}$n=0, k=0$ の混合ロスビー重力波の構造}{126}
\contentsline {section}{\numberline {13.2}$ n=0, k\not =0$ の東進混合ロスビー重力波}{132}
\contentsline {subsection}{\numberline {13.2.1}$ 0 < k \le 0.7$ (低波数)の場合}{132}
\contentsline {subsection}{\numberline {13.2.2}$ k > 0.7$ (高波数)の場合}{134}
\contentsline {section}{\numberline {13.3}$ n=0, k\not =0$ の西進混合ロスビー重力波}{136}
\contentsline {subsection}{\numberline {13.3.1}$ 0 < k \le 2.5$ (低波数)の場合}{136}
\contentsline {subsection}{\numberline {13.3.2}$ k > 2.5$ (高波数)の場合}{140}
\contentsline {chapter}{\numberline {14}赤道ケルビン波の水平伝播のメカニズム}{146}
\contentsline {chapter}{\numberline {A}赤道波の固有値・固有関数(有次元系)}{150}
\contentsline {section}{\numberline {A.1}固有値問題の定式化}{150}
\contentsline {section}{\numberline {A.2}固有値, 固有関数のまとめ}{151}
\contentsline {subsection}{\numberline {A.2.1}$ \mathaccent "705E {v}\not =0$ の解}{151}
\contentsline {subsection}{\numberline {A.2.2}$ \mathaccent "705E {v}=0$ の解}{151}
\contentsline {chapter}{\numberline {B}$n\ge 1$ の分散関係式の解}{152}
\contentsline {section}{\numberline {B.1}$ n\ge 1$ の場合の分散関係式の厳密解}{152}
\contentsline {section}{\numberline {B.2}$ n\ge 1$ の場合の分散関係式の近似解}{156}
\contentsline {subsection}{\numberline {B.2.1}Matsuno(1966)の方法}{157}
\contentsline {subsection}{\numberline {B.2.2}厳密解から近似解を導く方法}{157}
\contentsline {chapter}{\numberline {C}赤道波方程式の各項のモード展開}{160}
\contentsline {chapter}{\numberline {D}渦度方程式の各項のモード展開}{163}
\contentsline {chapter}{\numberline {E}回転の無い浅水系の重力波}{166}
\contentsline {section}{\numberline {E.1}1次元の非回転浅水系重力波}{166}
\contentsline {section}{\numberline {E.2}2次元の非回転浅水系重力波}{167}
\contentsline {chapter}{\numberline {F}$ n=1, k\not =0$ の慣性重力波の構造を決める物理量}{175}
\contentsline {chapter}{\numberline {G}$ n=2, k=0$ の慣性重力波の構造を決める物理量}{177}
\contentsline {chapter}{\numberline {H}$ n=0, k=0$ の混合ロスビー重力波の構造を決める物理量}{179}